The striker, who received his first call-up to the Argentina squad last week, will be a free agent at the end of the season.
"I'm pretty confident [that he will stay]," said Martinez.
"If I'm honest, we haven't even looked into it yet in detail. We have had conversations as we always have with all the players as they get into that situation but we all know what we want and what we want is to carry on with the development."
Di Santo has scored three goals in nine games for Wigan this season.